Examine the pattern of tiles below.

1. On graph paper, draw Figures 4 and 5.

   Hint (a):

   Figure 1 is a $2$-by-$2$ square.
   Figure 2 is a $3$-by-$3$ square.
   Figure 3 is a $4$-by-$4$ square.
   That means Figure $x$ should be a $(x + 1)-\text{by}-(x + 1)$ square.

2. What would Figure 10 look like? How many tiles would it have on each side? What about Figure 100?

   Hint (b):

   Refer to part (a).

   Answer (b):

   Figure 10: An $11$-by-$11$ square that would have $121$ tiles.
   Can you use the pattern to find what Figure 100 would look like?

3. Cami has a different pattern. She decided to represent the number of tiles in her pattern in a table, as shown below. Can you use the table to predict how many tiles would be in Figure 5 of her tile pattern? How many tiles would Figure 8 have? Explain how you know.